[PL 211] The Pixies and hypothetical syllogisms

Pure hypothetical syllogisms are syllogisms with two premises and a conclusion that are conditional statements. For example:

1. If the man is five, then the devil is six.
2. If the devil is six, then god is seven.
3. Therefore, if the man is five, then god is seven.

Is this form of inference always valid?

Consider the following:

1. If I am listening to the Pixies, then I am listening to a band whose name starts with the letter 'P'.
2. If I am listening to a band whose name starts with the letter 'P', then I could be listening to the Police.
3. Therefore, if I am listening to the Pixies, then I could be listening to the Police.

Is this hypothetical syllogism valid or invalid?